The 'Jules Margottin' parentage is correct (I don't know where the Rosenlexikon came up with the Jacqueminot parentage), as it is attested all the way back pre-introduction in 1861: "Mr. W. Paul contributed a seedling Rose raised from ‘Jules Margottin’, of good properties and vigorous habit, of a bright rosy crimson shade of colour, good shape, cupped, and of good substance of petal. He proposed to call it ‘Beauty of Waltham Cross’. For this a first-class Certificate was awarded” (Gardeners’ Chronicle, 1861, vol. 21, p. 578; the name was shortened upon actual introduction the next year).

I do see that, in 1862, "D., of Deal" speculates that the other parent was ‘Général Jacqueminot’: "It seemed to be a cross between ‘Jules Margottin’ and ‘Général Jacqueminot’, partaking of the excellent qualities of both parents" (Journal of Horticulture, vol. III, 1862, p. 42); however, that was just speculation on his part. I've seen a bit of "D., of Deal" in my researches over time; and he was, shall we say, a bit of a controversialist.

The Rose Garden. (2nd edition 1863) William Paul
Page 191-192
The term “cupped” is applaid in cases where the outer petals of the flower stand erect, or are slightly incurved, the petals within being in general of smaller size than the outer ones, the flower thus being a little hollow in the centre like a cup. Examples of this term: Madame Hardy (Damask), Coupe d’Hebe (Hybrid Bourbon), Auguste Mie, Beauty of Waltham, Louise Peyronny (Hybrid Perpetuals)